For time series modeling, many prior publications have extended VAE in a sequential manner [1]}, [2]}, [3]}, [4]}. The main idea is to use a deterministic Recurrent Neural Network (RNN) as a backbone, represented by the sequence of RNN hidden states. At each timestamp, the RNN hidden state is conditioned on the previous observation \(\mathbf {x}_{t-1}\)  and stochastic latent variable \(\mathbf {z}_{t-1}\) , such that the model is able to capture sequential features from time series data.
